Color groups of colorings of N-planar modules

A submodule of a -module determines a coloring of the module where each coset of the submodule is associated to a unique color. Given a submodule coloring of a -module, the group formed by the symmetries of the module that induces a permutation of colors is referred to as the color group of the colo...

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Bibliographic Details
Published in:Journal of physics. Conference series 2017-02, Vol.809 (1), p.12029
Main Authors: Loquias, Manuel Joseph C., Valdez, Lilibeth D., Walo, Ma. Lailani B.
Format: Article
Language:English
Subjects:
Apexes
Color
Coloring
Group theory
Lattices
Modules
Permutations
Physics
Tiling
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Summary:A submodule of a -module determines a coloring of the module where each coset of the submodule is associated to a unique color. Given a submodule coloring of a -module, the group formed by the symmetries of the module that induces a permutation of colors is referred to as the color group of the coloring. In this contribution, a method to solve for the color groups of colorings of N-planar modules where N = 4 and N = 6 are given. Examples of colorings of rectangular lattices and of the vertices of the Ammann-Beenker tiling are given to exhibit how these methods may be extended to the general case.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/809/1/012029